Semiparametric lag dependent functions

Abstract:
This paper introduces a suite of tests for linear and general non-

linear serial dependence. The problem is complex as the number of

variations of realistic non-linear alternatives is very large.

The alternative model is dened in terms of penalized truncated

polynomial splines, making the approximation capable of accurately

approximating a large class of linear and non-linear processes.

The asymptotic distribution for the test statistic is derived, and we

show using Monte Carlo simulations that one test is equivalent to the

Ljung-Box test, other linear tests corresponds to ordinary or partial

sample autocorrelation while the non-linear versions are capable of de-

tecting non-linear eects, even when other tests fail to do so.